Salah A. Khafagy, Hassan M. Serag
Abstract:
We study the maximum principle and existence of positive solutions for the
nonlinear system
\begin{gather*}
-\Delta _{p,_{P}}u=a(x)|u|^{p-2}u+b(x)|u|^{\alpha }|v|^{\beta }v+f \quad
\text{in } \Omega , \\
-\Delta _{Q,q}v=c(x)|u|^{\alpha }|v|^{\beta }u+d(x)|v|^{q-2}v+g \quad
\text{in } \Omega , \\
u=v=0 \quad \text{on }\partial \Omega ,
\end{gather*}
where the degenerate p-Laplacian defined as
.
We give necessary and sufficient
conditions for having the maximum principle for this system and then we
prove the existence of positive solutions for the same system by using an
approximation method.